Global Value Numbering
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Global Value Numbering
Value numbering is a technique of determining when two computations in a program are equivalent and eliminating one of them with a semantics-preserving optimization. Global value numbering Global value numbering (GVN) is a compiler optimization based on the static single assignment form (SSA) intermediate representation. It sometimes helps eliminate redundant code that common subexpression elimination (CSE) does not. At the same time, however, CSE may eliminate code that GVN does not, so both are often found in modern compilers. Global value numbering is distinct from local value numbering in that the value-number mappings hold across basic block boundaries as well, and different algorithms are used to compute the mappings. Global value numbering works by assigning a value number to variables and expressions. The same value number is assigned to those variables and expressions which are provably equivalent. For instance, in the following code: w := 3 x := 3 y := x + 4 z := ...
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Computations
Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An especially well-known discipline of the study of computation is computer science. Physical process of Computation Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers. This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing. An even more radical point of view, pancomputationalism (inaudible word), is the postulate of digital physics that argues that the evolution of the universe is itself a ...
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Pseudocode
In computer science, pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading. It typically omits details that are essential for machine understanding of the algorithm, such as variable declarations and language-specific code. The programming language is augmented with natural language description details, where convenient, or with compact mathematical notation. The purpose of using pseudocode is that it is easier for people to understand than conventional programming language code, and that it is an efficient and environment-independent description of the key principles of an algorithm. It is commonly used in textbooks and scientific publications to document algorithms and in planning of software and other algorithms. No broad standard for pseudocode syntax exists, as a program in pseudocode is not an executa ...
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POPL
The annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL) is an academic conference in the field of computer science, with focus on fundamental principles in the design, definition, analysis, and implementation of programming languages, programming systems, and programming interfaces. The venue is jointly sponsored by two Special Interest Groups of the Association for Computing Machinery: SIGPLAN and SIGACT. POPL ranks as A* (top 4%) in the CORE conference ranking. The proceedings of the conference are hosted at the ACM Digital Library. They were initially under a paywall, but since 2017 they are published in open access as part of the journal ''Proceedings of the ACM on Programming Languages'' (PACMPL). Affiliated events * Declarative Aspects of Multicore Programming (DAMP) * Foundations and Developments of Object-Oriented Languages (FOOL/WOOD) * Partial Evaluation and Semantics-Based Program Manipulation (PEPM) * Practical Applications of Decl ...
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Common Subexpression Elimination
In compiler theory, common subexpression elimination (CSE) is a compiler optimization that searches for instances of identical expressions (i.e., they all evaluate to the same value), and analyzes whether it is worthwhile replacing them with a single variable holding the computed value. Example In the following code: a = b * c + g; d = b * c * e; it may be worth transforming the code to: tmp = b * c; a = tmp + g; d = tmp * e; if the cost of storing and retrieving tmp is less than the cost of calculating b * c an extra time. Principle The possibility to perform CSE is based on available expression analysis (a data flow analysis). An expression b*c is available at a point ''p'' in a program if: * every path from the initial node to p evaluates b*c before reaching ''p'', * and there are no assignments to b or c after the evaluation but before ''p''. The cost/benefit analysis performed by an optimizer will calculate whether the cost of the store to tmp is less than the c ...
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Optimizing Compiler
In computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of ''optimizing transformations'', algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster. It has been shown that some code optimization problems are NP-complete, or even undecidable. In practice, factors such as the programmer's willingness to wait for the compiler to complete its task place upper limits on the optimizations that a compiler might provide. Optimization is generally a very CPU- and memory-intensive process. In the past, computer memory limitations were also a major factor in limiting which optimizations coul ...
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Partial Redundancy Elimination
In compiler theory, partial redundancy elimination (PRE) is a compiler optimization that eliminates expressions that are redundant on some but not necessarily all paths through a program. PRE is a form of common subexpression elimination. An expression is called partially redundant if the value computed by the expression is already available on some but not all paths through a program to that expression. An expression is fully redundant if the value computed by the expression is available on all paths through the program to that expression. PRE can eliminate partially redundant expressions by inserting the partially redundant expression on the paths that do not already compute it, thereby making the partially redundant expression fully redundant. For instance, in the following code: if (some_condition) else z = x + 4; the expression x+4 assigned to z is partially redundant because it is computed twice if some_condition is true. PRE would perform code motion on the expres ...
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Bitwise AND
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signif ...
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Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and  are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ...
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Basic Block
In compiler construction, a basic block is a straight-line code sequence with no branches in except to the entry and no branches out except at the exit. This restricted form makes a basic block highly amenable to analysis. Compilers usually decompose programs into their basic blocks as a first step in the analysis process. Basic blocks form the vertices or nodes in a control-flow graph. Definition The code in a basic block has: * One entry point, meaning that no code within it is the destination of a jump instruction anywhere in the program. * One exit point, meaning that only the last instruction can cause the program to begin executing code in a different basic block. Under these circumstances, whenever the first instruction in a basic block is executed, the rest of the instructions are necessarily executed exactly once and in order. The code may be source code, assembly code, or some other sequence of instructions. More formally, a sequence of instructions forms a basic block ...
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Compiler Optimization
In computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of ''optimizing transformations'', algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster. It has been shown that some code optimization problems are NP-complete, or even undecidable. In practice, factors such as the programmer's willingness to wait for the compiler to complete its task place upper limits on the optimizations that a compiler might provide. Optimization is generally a very CPU- and memory-intensive process. In the past, computer memory limitations were also a major factor in limiting which optimizations co ...
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Global Value Numbering
Value numbering is a technique of determining when two computations in a program are equivalent and eliminating one of them with a semantics-preserving optimization. Global value numbering Global value numbering (GVN) is a compiler optimization based on the static single assignment form (SSA) intermediate representation. It sometimes helps eliminate redundant code that common subexpression elimination (CSE) does not. At the same time, however, CSE may eliminate code that GVN does not, so both are often found in modern compilers. Global value numbering is distinct from local value numbering in that the value-number mappings hold across basic block boundaries as well, and different algorithms are used to compute the mappings. Global value numbering works by assigning a value number to variables and expressions. The same value number is assigned to those variables and expressions which are provably equivalent. For instance, in the following code: w := 3 x := 3 y := x + 4 z := ...
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Copy Propagation
In compiler theory, copy propagation is the process of replacing the occurrences of targets of direct assignments with their values. A direct assignment is an instruction of the form x = y, which simply assigns the value of y to x. From the following code: y = x z = 3 + y Copy propagation would yield: z = 3 + x Copy propagation often makes use of reaching definitions, use-def chains and def-use chains when computing which occurrences of the target may be safely replaced. If all upwards exposed uses of the target may be safely modified, the assignment operation may be eliminated. Copy propagation is a useful "clean up" optimization frequently used after other compiler passes have already been run. Some optimizations—such as classical implementations of elimination of common sub expressions—''require'' that copy propagation be run afterwards in order to achieve an increase in efficiency. See also * Copy elision In C++ computer programming, copy elision refers to a ...
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